Many people often wonder: What’s the difference between a wallet and an address? Are they the same and if not, how do they differ?
The short answer is that they are two different things, with the address being the ID of where the Bitcoins are being held, while the wallet is program controlling the address and facilitating transfers to and from the address.
Explaining it more in depth:
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An address is a Bitcoin public key to which transactions can be sent. It represents the public key of an asymmetric key pair. The private key of this “key pair” is used to sign transactions or otherwise prove ownership of an account. A signature can only be created if the correct private key is used. The signature can then be verified by anyone by using the associated address (i.e. “the public key”).
A wallet, on the other hand, is a collection of private keys that correspond to addresses. It is the data needed in order to receive and spend bitcoins The Bitcoin client software checks each of the addresses contained in the wallet and whether there are any balances/transactions associated in the blockchain with them. It then calculates the total balance. The wallet is generally a text file on disk and often includes important features such as encryption and address labeling. (More about Bitcoin wallets)
From a technical perspective, Bitcoins are sent and received from an address. One encrypts, exports, backs up, and imports from a wallet. The relationship between a wallet and an address is often compared to a key (the address) and key ring (the wallet).